Question

using the unit circle, calculate the value of sin 240°. (1 point)
(\frac{sqrt{3}}{2})
(\frac{1}{2})
(-\frac{sqrt{3}}{2})
(-\frac{sqrt{2}}{2})

Explanation:

Step1: Determine the reference angle

First, we find the reference angle for \(240^\circ\). Since \(240^\circ\) is in the third quadrant (\(180^\circ < 240^\circ < 270^\circ\)), we subtract \(180^\circ\) from \(240^\circ\) to get the reference angle:
\(240^\circ - 180^\circ = 60^\circ\).

Step2: Recall the sine value of the reference angle

We know that \(\sin 60^\circ = \frac{\sqrt{3}}{2}\).

Step3: Determine the sign of \(\sin 240^\circ\)

In the third quadrant, both sine and cosine are negative (since \(y\)-coordinates on the unit circle are negative here). So, \(\sin 240^\circ\) will be the negative of \(\sin 60^\circ\).

Thus, \(\sin 240^\circ = -\sin 60^\circ = -\frac{\sqrt{3}}{2}\).

Answer:

\(-\frac{\sqrt{3}}{2}\) (corresponding to the option with \(-\frac{\sqrt{3}}{2}\))